Multiple Weather Station Analysis
Process We constructed econometric formulations for a few states with multiple weather stations using the data from last year this provides for a comparison to last year s models This resulted in problems with model coefficients of the wrong sign and with variables that were not statistically significant 2
2014 TX Model (San Antonio) Dependent Variable: ELECTRICITY_SALES Method: Least Squares Date: 03/13/15 Time: 15:42 Sample: 1990 2012 Included observations: 23 Variable Coefficient Std. Error t-statistic Prob. C 30527.38 33755.29 0.904373 0.3784 @MOVAV(REAL_ELECTRICITY_PRICE,5) -4641.131 1375.351-3.374506 0.0036 REAL_INCOME/POPULATION 3515.000 1454.605 2.416465 0.0272 REAL_GSP 0.145494 0.026098 5.574822 0.0000 CDD 16.16171 3.823118 4.227363 0.0006 HDD 20.84670 5.074099 4.108454 0.0007 R-squared 0.993627 Mean dependent var 307551.8 Adjusted R-squared 0.991752 S.D. dependent var 43037.33 S.E. of regression 3908.547 Akaike info criterion 19.59918 Sum squared resid 2.60E+08 Schwarz criterion 19.89539 Log likelihood -219.3905 Hannan-Quinn criter. 19.67367 F-statistic 530.0731 Durbin-Watson stat 1.629527 Prob(F-statistic) 0.000000 3
2014 TX (multiple stations) Dependent Variable: ELECTRICITY_SALES Method: Least Squares Sample: 1990 2012 Included observations: 23 Variable Coefficient Std. Error t-statistic Prob. C -9940.844 34462.99-0.288450 0.7784 @MOVAV(REAL_ELECTRICITY_PRICE,5) -3619.431 1297.105-2.790392 0.0176 REAL_INCOME/POPULATION 5110.873 1386.709 3.685613 0.0036 REAL_GSP 0.105381 0.026246 4.015128 0.0020 DALLAS_TX_C 9.074900 5.438765 1.668559 0.1234 DALLAS_TX_H -5.838066 8.363243-0.698063 0.4996 HOUSTON_TX_C 7.655999 6.386797 1.198723 0.2558 HOUSTON_TX_H 28.83526 12.32312 2.339931 0.0392 LUBBOCK_TX C 2.291983 7.991036 0.286819 0.7796 LUBBOCK_TX H 3.467606 7.266146 0.477228 0.6425 SAN_ANTONIO_TX_C 5.075477 6.074335 0.835561 0.4212 SAN_ANTONIO_TX_H -4.522494 13.89882-0.325387 0.7510 R-squared 0.997415 Mean dependent var 307551.8 Adjusted R-squared 0.994829 S.D. dependent var 43037.33 S.E. of regression 3094.724 Akaike info criterion 19.21866 Sum squared resid 1.05E+08 Schwarz criterion 19.81110 Log likelihood -209.0146 Hannan-Quinn criter. 19.36766 F-statistic 385.7912 Durbin-Watson stat 1.950824 Prob(F-statistic) 0.000000 4
HDD Correlations Dallas Houston Lubbock San Antonio Dallas - 0.90 0.79 0.87 Houston 0.90-0.70 0.88 Lubbock 0.79 0.70-0.80 San Antonio 0.87 0.88 0.80-5
A Different Process We developed virtual weather stations using population-weighted CDD and HDD from multiple weather stations within the states Each state is divided into regions along county lines and a representative weather station is chosen for each region The CDD and HDD for a given year are determined using the population of each region and the CDD and HDD of the region s weather station 6
2014 TX (virtual station) Dependent Variable: ELECTRICITY_SALES Method: Least Squares Date: 03/13/15 Time: 15:42 Sample: 1990 2012 Included observations: 23 Variable Coefficient Std. Error t-statistic Prob. C 18197.81 29241.15 0.622336 0.5420 @MOVAV(REAL_ELECTRICITY_PRICE,5) -3792.856 1121.703-3.381337 0.0035 REAL_INCOME/POPULATION 3605.803 1238.386 2.911695 0.0097 REAL_GSP 0.137162 0.022457 6.107792 0.0000 CDDMWS 20.02943 3.703811 5.407790 0.0000 HDDMWS 16.95795 3.897780 4.350669 0.0004 R-squared 0.995288 Mean dependent var 307551.8 Adjusted R-squared 0.993902 S.D. dependent var 43037.33 S.E. of regression 3360.723 Akaike info criterion 19.29716 Sum squared resid 1.92E+08 Schwarz criterion 19.59337 Log likelihood -215.9173 Hannan-Quinn criter. 19.37166 F-statistic 718.1691 Durbin-Watson stat 1.598551 Prob(F-statistic) 0.000000 7
Model Comparison TX Comparison across models Single weather station Populationweighted average weather Multiple weather stations Adjusted R-squared 0.992 0.994 0.995 Prob(F-statistic) 0.000 0.000 0.000 Durbin-Watson stat 1.630 1.599 1.951 Mean absolute error 2685.298 2276.612 1696.387 8
510,000 460,000 410,000 360,000 310,000 260,000 210,000 ENERGY CENTER TX Model Comparison Texas 2024 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 History 2014 model forecast - single weather station 2014 model forecast - population weighted average weather 9 Annual retail sales in GWh
170000 160000 150000 140000 130000 120000 110000 ENERGY CENTER IL Model Comparison 10 Annual retail sales in GWh 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 Illinois History 2014 model forecast - single weather station 2014 model forecast - population weighted average weather
135,000 125,000 115,000 105,000 95,000 85,000 75,000 65,000 ENERGY CENTER IN Model Comparison Indiana 11 Annual retail sales in GWh 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 History 2014 model forecast - single weather station 2014 model forecast - population weighted average weather
95000 90000 85000 80000 75000 70000 65000 60000 ENERGY CENTER LA Model Comparison 12 Annual retail sales in GWh 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 Louisiana History 2014 model forecast - single weather station 2014 model forecast - population weighted average weather
130000 125000 120000 115000 110000 105000 100000 95000 90000 85000 80000 ENERGY CENTER MI Model Comparison Michigan 2024 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 13 History 2014 model forecast - single weather station 2014 model forecast - population weighted average weather Annual retail sales in GWh
Results We examined the possibility of using multiple weather stations (each as a separate variable) and found it infeasible We believe that the population-weighted virtual station works well but has little impact on the forecast results We propose to use the populationweighted virtual station method 14
Population Weighted Virtual Weather Stations Orange indicates a weather station that is used Blue indicates a weather station that could not be used because of data problems
Arkansas Population Density Map Fayetteville Harrison Little Rock Source: US Census Bureau 16
Iowa Population Density Map Waterloo Cedar Rapids Des Moines Iowa City 17
Illinois Population Density Map Chicago Springfield Carbondale 18
Indiana Population Density Map South Bend Evansville Indianapolis 19
Kentucky Population Density Map Henderson Lexington Paducah Bowling Green 20
Louisiana Population Density Map Shreveport New Orleans Source: "Arkansas population map" by Jim Irwin at the English language Wikipedia. 21
Michigan Population Density Map Marquette Munising Grand Rapids Detroit 22
Minnesota Population Density Map Thief River Falls Duluth Fergus Falls Minneapolis 23
Missouri Population Density Map Kansas City St. Louis Springfield 24
Mississippi Population Density Map Tupelo Jackson Hattiesburg Pascagoula Gulfport 25
Montana Population Density Map Missoula Billings 26
North Dakota Population Density Map Fargo Bismarck 27
South Dakota Population Density Map Rapid City Sioux Falls 28
Texas Population Density Map Lubbock Dallas Houston San Antonio 29
Wisconsin Population Density Map Green Bay Milwaukee 30